Chapter 4: Measuring motion

When studying physics, you’ll often find that the words we use in physics have slightly different meanings than when we use the same word in every day life. This is because when we’re communicating about science we need to be more specific and precise, to limit ambiguity and make sure we’re communicating effectively.

In this chapter, we’ll focus on how we measure the motion of an object. This includes the concepts of position, velocity, and acceleration.

4.1 Position

If someone is trying to find you, and they ask where you are, it is unhelpful for you to simply say “I am here.” This gives them no information, other than the fact that you exist somewhere. You need to give them more information, such as saying “I’m across the street from the Starbucks” or “I’m on the corner of 4th and Pacific Avenue.”

Position gives the location of an object relative to some reference point. Mathematically, we’ll define the reference as the origin of a coordinate system. We typically use the Cartesian coordinate system, but we are free to define where the origin is, and which way is positive. We can choose anything we like, but we must stay consistent throughout any following calculations.

You need two pieces of information: distance from the origin, and direction. This means position is a vector quantity. The SI unit for position is the meter (m).

1D and 2D position

When we work with motion along a single axis, a positive or negative sign is all we need to indicate direction. It is common practice to use \(x\) to represent an object’s position on the horizontal (left/right) axis, and \(y\) to represent an object’s motion on the vertical (up/down) axis.

When dealing with two dimensional motion, we’ll need to use vector notation. Position in two dimensions is generally represented using vector notation.

Example

You are standing at the top of a 50 m deep hole in the ground that opens into an underground cavern. Your friend is exploring the cavern, and is at the bottom of the hole. If you define the ground as the origin of your coordinate system, and the positive y direction is up (towards the sky), your friend has a position \(y = -50\ \textrm{m}\).

Practice